Oscillatory focusing of particles in channels

ABSTRACT

This disclosure provides systems and methods to extend the capabilities of inertial and/or viscoelastic focusing in channels, such as microchannels. The new systems and methods can be integrated with existing microfluidic devices for inertial and/or viscoelastic manipulation of particles that have defied prior attempts, enabling a variety of applications in clinical diagnosis. The particles, e.g., bioparticles and cells, focus into streamlines in the same way and in the same locations as in existing inertial and viscoelastic focusing systems, but at much lower particle Reynolds numbers, much lower shear stress, over much shorter distances, and at lower driving pressures and/or flow rates.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Application Ser.No. 62/514,606, filed on Jun. 2, 2017. The entire content of theprovisional application is incorporated herein by reference.

STATEMENT AS TO FEDERALLY SPONSORED RESEARCH

This invention was made with Government support under 5P41EB002503-14and 5U01EB012493-07 awarded by the National Institutes ofHealth/National Institute of Biomedical Imaging and Bioengineering(NIH/NIBIB). The Government has certain rights in the invention.

TECHNICAL FIELD

This disclosure relates to inertial and viscoelastic microfluidics, andmore particularly to focusing of particles in channels, such asmicrochannels.

BACKGROUND

Inertial microfluidics (i.e., migration and focusing of particles infinite Reynolds number microchannel flows) is a passive, precise, andhigh-throughput method for microparticle manipulation and sorting.Therefore, it has been utilized in numerous biomedical applicationsincluding phenotypic cell screening, blood fractionation, and rare cellisolation. Nonetheless, the applications of this technology have beenlimited to larger particles such as blood cells, circulating tumorcells, and stem cells; because smaller particles require drasticallylonger channels for inertial focusing, which increases the pressurerequirement and the footprint of the device to the extent that thesystem becomes unfeasible. Inertial manipulation of smaller particlessuch as fungi, bacteria, viruses, and other pathogens, or bloodcomponents such as platelets and exosomes, is of significant interest.

Inertial microfluidics, which is the manipulation and focusing ofparticles in microchannels using inertial lift forces, has been employedin several key technologies since it was first demonstrated by Di Carloet al. in 2007 (Proc. Natl. Acad. Sci., 104(48) (2007)). First observedby Segre and Silberberg with millimeter-scale particles flowing througha large (˜1 cm) circular tube (Segré et al., Nature 189 (4760):209-210,1961), randomly distributed particles laterally migrate to equilibriumfocus positions (streamlines) that are pre-determined by the flowcharacteristics and the channel geometry. This inertial migrationenables passive and precise manipulation of particles in microchannels,and has been utilized for aligning, ordering, or separating target cellsin blood.

This technology has been used in various biomedical applications,including phenotypic cell screening, blood fractionation, and rare cell(e.g. circulating tumor cells) isolation. For example, Di Carlo et al.used asymmetric curves to achieve differential inertial focusing forseparation of larger blood cells (RBCs and WBCs) from platelets (Anal.Chem., 80(6):2204-2211, 2008). Lee et al. used a spiral geometry forsize-based separation based on cell cycle and DNA content (Lab Chip11(7):1359-1367, 2011). Sollier et al. employed sudden expansionchannels in combination with Vortex technology, to isolate CTCs fromwhole blood (Lab Chip 14(1):63-77, 2014). Ozkumur et al. used inertialfocusing in a multi-stage circulating tumor cell (CTC) isolation chip toalign and order nucleated cells after on-chip debulking of blood, tofacilitate magnetic separation of white blood cells from CTCs (Sci.Transl. Med., 5(179):179ra47, 2013).

Recently, three-dimensional stacking of chips has been explored, whichin return significantly improved the throughput of the devices (Warkianiet al., Nat. Protoc., 11(1):134-48 (2016) and Miller et al., Sci. Rep.,6(October):36386, 2016). Inertial microfluidics have also been used forsheathless alignment of cells for flow cytometry (Hur et al., Lab Chip10(3):274-280, 2010), size-based separation of white blood cells fromlysed blood (Gossett et al., Small, 8(17):2757-2764, 2012) and wholeblood fractionation (Mutlu et al., Sci. Rep., 7(1):9915, 2017), andseveral other applications as summarized in a review by Martel et al(Annu. Rev. Biomed. Eng., 16:371-96, 2014).

Despite the wide breadth of its applications, inertial microfluidics hasgenerally been confined to particles that are a few microns or larger(i.e., not smaller than a red blood cell), because of the strongcorrelation between the inertial lift forces and the particle size.Smaller particles travelling in typical microchannels (having across-sectional dimension of tens of microns) require drastically longerchannels for focusing (in the order of meters), increasing the pressurerequirement and the footprint of the channel to the extent that thesystem becomes unfeasible. Inertial manipulation of smaller bioparticlessuch as fungi, bacteria, and other pathogens, or blood components suchas extracellular microvesicles is of significant interest. For instance,identifying the infecting agent in a timely manner is crucial for thetreatment of septic patients. Furthermore, recent studies show thatexosomes carry information regarding primary tumor, and can help withcancer diagnostics (Skog et al., Nat. Cell Biol., 10(12):1470-6, 2008,and Melo et al., Nature, 523(7559): 177-182, 2015).

In one study, inertial focusing of 0.92 μm particles was reported inwiggler-shaped microchannels produced from a thermoset polyester (TPE)material (Wang et al., Adv. Sci., 2017, 4, 1700153) to withstand thevery high pressures required. One drawback of such high pressures andflow rates is that particles experience significant shear stress, whichcould be harmful or detrimental to bioparticles and cells. Additionally,higher pressures increase the risk of catastrophic failure, thus addingadditional cost for safe operation of the system. As a result,applications of inertial focusing of biological particles have generallybeen limited to larger biological particles (blood cells, circulatingtumor cells, stem cells, etc.).

SUMMARY

This disclosure provides systems and methods to extend the capabilitiesof inertial and/or viscoelastic focusing in channels, such asmicrochannels, to smaller particles, lower shear stresses, shorterchannels, and lower pressure drops, or any combination thereof. Thesenew systems and methods can be integrated with existing microfluidicdevices for inertial and/or viscoelastic manipulation of particles thathave defied all prior attempts, enabling a variety of applications inclinical diagnosis including cytometry of micron-scale particles,isolation and characterization of pathogens and extracellularmicrovesicles, or phenotyping of cancer or stem cells at physiologicalshear stresses. The particles, e.g., bioparticles and cells, focus intostreamlines in the same way and in the same locations as in existinginertial and viscoelastic focusing systems, but at much lower particleReynolds numbers, much lower shear stress, over much shorter distancesand at lower driving pressures and/or flow rates.

In one aspect, the disclosure provides oscillatory fluidic systems forfocusing of particles in a fluid sample into one or more streamlineswithin a fluid flowing in a channel. The systems include a fluidoscillator for alternating a direction of flow of the fluid in achannel; and a controller arranged and configured to transmit controlsignals to the fluid oscillator to generate a repeating oscillating flowprofile of the fluid sample in the channel, wherein the flow profileincludes at least one step in a first direction of flow and at least onestep in a second direction of flow opposite to the first direction offlow, for a set period of time, thereby focusing the particles into oneor more streamlines within the fluid flowing within the channel.

These systems can further include a millimeter or micrometer channel.The dimensions of the channel and the controller can be configured toprovide inertial focusing and/or viscoelastic focusing. The viscoelasticfocusing occurs when a fluid in the channel is selected to have anappropriate viscosity.

The systems can include a fluid oscillator that includes a source ofpressure or flow arranged and controlled to provide an oscillatingpressure on, or flow of, the fluid to provide the oscillating flowwithin the channel. In other implementations, the systems can include afluid oscillator that includes a source of constant pressure or constantflow arranged and controlled to provide a constant pressure on, orconstant flow of, the fluid within the channel and the fluid oscillatorfurther comprises two or more valves arranged along the channel andcontrolled to provide the oscillating flow within the channel betweenthe two or more valves by directing the constant pressure or flow fromthe source alternatingly at a first location along the channel and thenat a second location along the channel.

In some implementations, the fluid oscillator can further include asignal (pulse) generator and a valve driving circuit, and the two ormore valves can be high-speed, three-way valves.

In some implementations, the channel dimensions are configured and theflow rate of the fluid in the channel is controlled such that a Reynoldsnumber within the channel in each direction of flow is from about 0.01to 2300 (Re_(p) is also less than 2300, e.g., from about 0.1 to about100, e.g., 0.01 to 10.0 or 0.01 to 1.0). In some implementations, theReynolds number within the microfluidic channel in each direction offlow is from about 0.1 to 100. In certain embodiments, the frequency ofoscillations is from about 0.01 Hertz to about 100 Hertz.

In some implementations, particles flowing within the fluid move adistance of 1.0 micron to 100 cm in the first direction of flow, andthen 1.0 micron to 100 cm in the second direction of flow. For example,the particles flowing within the fluid move a distance of 10 microns to10 cm in the first direction of flow, and then 10 microns to 10 cm inthe second direction of flow. In some embodiments, particles flowingwithin the fluid move a first distance in one direction a seconddistance in the opposite direction. For example, the first distance canbe the same as the second distance, and thus the particles remain withinone location within the channel. Alternatively, the first distance isgreater than the second distance, such that the particles move from afirst location within the channel to a second location within thechannel.

In some implementations, the fluid oscillator is controlled to controlthe flow of the fluid in the channel to achieve a particle Reynoldsnumber greater than about 0.001. In some embodiments, the hydraulicdiameter (D_(h)) of the channel is selected to achieve a ratio ofparticle diameter a to D_(h) to be greater than 0.001 and less than 1.0.

In some implementations, the channel comprises a first section having afirst hydraulic diameter, a second section in series with the firstsection and having a second hydraulic diameter smaller than the firsthydraulic diameter, and a third section in series with the secondsection and having a third hydraulic diameter larger than the secondhydraulic diameter.

In various implementations, the system is configured to have at leastone, e.g., two or more in any combination, of the following parameters:a particle Reynolds number (Re_(p)) greater than about 0.002; a channelReynolds number (Re) less than about 2300; a channel hydraulic diameter(D_(h)) larger than a particle diameter a; a ratio of particle diametera to D_(h) less than about 1; and a Womersley number (Wo) less thanabout 1.

In another aspect, the disclosure provides methods for focusing ofparticles in a fluid sample into one or more streamlines within a fluidflowing within a channel. The methods include introducing into a channela fluid comprising particles to be focused; and controlling a flow rateof the fluid in the channel to generate a repeating oscillating flowprofile of the fluid in the channel, wherein the flow profile includesat least one step in a first direction of flow and at least one step ina second direction of flow opposite to the first direction of flow, fora set period of time; thereby focusing the particles into one or morestreamlines within the fluid flowing within the channel. The channel canbe a millimeter or micrometer channel, and the dimensions of the channeland the flow rate can be configured to provide inertial focusing orviscoelastic focusing when a fluid in the channel is selected to have anappropriate viscosity.

In some embodiments, controlling a flow rate of the fluid includesproviding a source of pressure or flow and controlling the source ofpressure or flow to provide the oscillating flow within the channel. Inother embodiments, controlling the flow rate of the fluid includesproviding a source of constant pressure or constant flow to provide aconstant pressure on, or constant flow of, the fluid within the channel,and controlling two or more valves arranged along the channel to providean oscillating flow within the channel between the two or more valves bydirecting the constant pressure or flow from the source alternatingly ata first location along the channel and then at a second location alongthe channel.

In some implementations, the channel dimensions are configured and theflow rate of the fluid in the channel is controlled such that a Reynoldsnumber within the channel in each direction of flow is from about 0.01to 2300, e.g., the Reynolds number within the channel in each directionof flow is from about 0.1 to 100 (Re_(p) is also less than 2300, e.g.,from about 0.1 to about 100, e.g., 0.01 to 10.0 or 0.01 to 1.0).

In some embodiments, the frequency of oscillations is from about 0.01Hertz to about 100 Hertz, and/or the particles flowing within the fluidmove a distance of 1.0 micron to 100 cm in the first direction of flow,and then 1.0 micron to 100 cm in the second direction of flow. Forexample, the particles flowing within the fluid move a distance of 10microns to 10 cm in the first direction of flow, and then 10 microns to10 cm in the second direction of flow.

In some implementations, particles flowing within the fluid move a firstdistance in one direction a second distance in the opposite direction.For example, the first distance can be the same as the second distance,and thus the particles remain within one location within the channel.Alternatively, the first distance can be greater than the seconddistance, such that the particles move from a first location within thechannel to a second location within the channel.

In some implementations, the fluid oscillator is controlled to controlthe flow of the fluid in the channel to achieve a particle Reynoldsnumber greater than about 0.001. In some embodiments, the hydraulicdiameter (D_(h)) of the channel is selected to achieve a ratio ofparticle diameter a to D_(h) to be greater than 0.001 and less than 1.0.In various implementations, the flow rate and channel dimensions areselected and/or controlled to achieve at least one, e.g., two or more inany combination, of the following parameters: a particle Reynolds number(Re_(p)) greater than about 0.002; a channel Reynolds number (Re) lessthan about 2300; a channel hydraulic diameter (D_(h)) larger than aparticle diameter a; a ratio of particle diameter a to D_(h) less thanabout 1; and a Womersley number (Wo) less than about 1.

The new systems and methods can be used to achieve inertial focusing inpractically “infinite channels,” allowing focusing of submicron-scale(i.e., hundreds of nanometers) particles. The new systems and methodsenable the manipulation of particles at extremely low particle Reynoldsnumber (Re_(p)<0.005), flows that are otherwise unattainable bysteady-flow inertial microfluidics (which has been limited toRe_(p)>about 0.1). Using these techniques, particles as small as about500 nm can be inertially focused.

As used herein a millimeter channel, has internal dimensions on theorder of millimeters, e.g., 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or moremillimeters in height and/or width. As used herein a micrometer channel,has internal dimensions on the order of micrometers, e.g., 1, 2, 3, 4,5, 6, 7, 8, 9, 10, 15, 20, 30, 40, 50, 60, 70, 80, 90, 100, 250, 500,750, or more micrometers in height and/or width.

Unless otherwise defined, all technical and scientific terms used hereinhave the same meaning as commonly understood by one of ordinary skill inthe art to which this invention belongs. Although methods and materialssimilar or equivalent to those described herein can be used in thepractice or testing of the present invention, suitable methods andmaterials are described below. All publications, patent applications,patents, and other references mentioned herein are incorporated byreference in their entirety. In case of conflict, the presentspecification, including definitions, will control. In addition, thematerials, methods, and examples are illustrative only and not intendedto be limiting.

The details of one or more embodiments of the disclosure are set forthin the accompanying drawings and the description below. Other featuresand advantages of the disclosure will be apparent from the followingdetailed description, and from the claims.

DESCRIPTION OF DRAWINGS

FIG. 1A is a schematic diagram of oscillatory inertial microfluidicstheory showing that inertial lift forces (F_(W) and F_(SG)) preservetheir directionality when the velocity field is reversed, enablingindefinite extension of the inertial focus length. It is also true thatthe directionality of lift forces remain the same when reversing thedirection of fluid motion in viscoelastic focusing as well, such thatoscillatory viscoelastic focusing is also possible as described herein.

FIG. 1B is a design schematic of the oscillatory microfluidics systemsused for oscillatory inertial focusing.

FIG. 2 is a schematic diagram of a control method and microchip foroscillatory inertial focusing, in which input pressures or flows arecontrolled according to a pressure or flow control signal.

FIG. 3 is a schematic diagram of a control method and microchip foroscillatory inertial focusing, in which input pressure or flow is steadyand valves and/or fluid resistance/capacitance (RC) components externalto the microchip are controlled to cycle the input pressure or flowaccording to inputs from a signal generator.

FIG. 4 is a schematic diagram of a control method and microchip foroscillatory inertial focusing, in which input pressure or flow is steadyand integrated valves and/or fluid resistance/capacitance (RC)components that are located within the microchip are controlled to cyclethe input pressure or flow according to inputs from a signal generator.

FIG. 5A is a schematic diagram of a “dog-bone” microchannel on amicrochip module that provides side or center streamline focusing ofwaste or product for concentrating a product.

FIG. 5B is a schematic diagram of a sinusoidal inertial focusing modulethat focuses product in streamlines at the side walls of the module forconcentrating a product.

FIGS. 5C and 5D are schematic diagrams showing the inputs and outputsfor the concentration chip modules of FIGS. 5A and 5B.

FIG. 5E is a graph of sample and waste/product streams and reservoirpressure over time.

FIG. 6A is a schematic diagram of a non-equilibrium inertial separationarray in a microchannel on a microchip module that provides sidewallstreamline focusing of waste and product for separation of a productfrom a sample.

FIG. 6B is a schematic diagram of a spiral inertial focusing module thatfocuses product in a streamline at a sidewall of the module forseparating the product from a sample.

FIGS. 6C and 6D are schematic diagrams showing the inputs and outputsfor the separation chip modules of FIGS. 6A and 6B, in forward andreverse flow, respectively.

FIG. 6E is a graph of sample and waste/product streams and reservoirpressure over time.

FIG. 7A is a pair of schematic diagrams showing the inputs and outputsfor a focusing chip modules used in intermittent flow for focusing aproduct using oscillatory flow, in forward and reverse flow,respectively, and a graph of sample and waste streams and reservoirpressure over time.

FIG. 7B is a schematic diagram showing the inputs and outputs for afocusing chip module used in intermittent flow for concentrating aproduct using steady flow, and a graph of sample and waste streams andreservoir pressure over time.

FIG. 8A is a pair of schematic diagrams showing the inputs and outputsfor a focusing chip module with a filter used in intermittent flow forcleaning the filter using oscillatory flow, in forward and reverse flow,respectively.

FIG. 8B is a pair of schematic diagrams showing the inputs and outputsfor a focusing chip module with a filter used in intermittent flow topurge the filtrate and for steady water filtration, in a brief forwardflow and a steady forward flow, respectively.

FIG. 8C is a graph of dirty water and waste streams and reservoirpressures over time.

FIG. 8D is a schematic of flows of dirty water and focused particles inPhases 0, 1, and 2 in a filter module.

FIGS. 9A and 9B are a pair of schematic diagrams of two ports on acytometry chip module used for long duration flow cytometry at acontrolled shear rate, in the forward and reverse flow modes,respectively.

FIG. 9C is a schematic diagram of two low resistance input/outputchannels separated by multiple thin microchannels for focusing. Theinput/output channels are relatively “thick,” e.g., have a largecross-sectional diameter, and the microchannels have a short length andhave a relatively narrow cross-sectional diameter. The short lengthensures a low pressure drop along the length of these microchannels.

FIG. 9D is a graph of Port 1 and 2 flows and reservoir pressures overtime.

FIG. 10A is a schematic graph of reciprocating motion to achieve highrpm oscillatory flow over time.

FIG. 10B is a schematic diagram of a microchip with three fluidreservoirs arranged along the microchip for sample input, buffer input,output, etc. and a piston in each reservoir to generate oscillatingpressures. These pressures are sinusoidal rather than square waves,though other continuously varying pressure profiles are possible withreciprocating machinery driven oscillatory flow.

FIG. 11A is a series of streak images of inertial focusing of particlesusing oscillatory microfluidics to oscillate 3.1 μm particles at thesame position in a microfluidic device (H=80 μm) over time (scale bar=50μm).

FIG. 11B is an intensity profile graph of the oscillating particles asthey become focused.

FIG. 11C is a graph showing full width half-maximum (FWHM) analysis overtime, used for determining the focus time.

FIGS. 12A and 12B are a pair of graphs showing attained focus times(14A) and focus lengths (14B) of 3.1 to 10 μm particles at varyingRe_(p).

FIG. 13A is a graph showing various parameters of oscillatory inertialfocusing including an upper limit of Reynolds number (Re) of about 2300,a particle Reynolds number (Re_(p)) of greater than 0.002, and a ratioof particle diameter (a) to hydraulic diameter (D_(h)) in a range ofabout 0.001<a/D_(h)<about 0.5 to 1.0.

FIG. 13B is a graph showing oscillation frequency and D_(h) space inwhich oscillatory inertial focusing works, i.e., where the Womersleynumber (Wo) is as large as 2.0 (but is typically less than 1.0).

FIG. 14A is a streak image showing oscillatory inertial focusing withdiffusion limitation in a microchannel (L=6.2 cm, H=40 μm) with thefocused 2 μm (and 1 μm) particles after t_(f) and their correspondingRep values.

FIG. 14B is graph showing the FWHM evolution profiles of 2 μm particlesfrom Re_(p)=0.0025 to 0.0125 (dot sign), and 1 μm particles atRe_(p)=0.0031 (plus sign).

FIG. 14C is a pair of streak images of the microchannel (L=2 cm, H=80μm) before and after focusing bacteria (0.8 μm) Staphylococcus aureus.

FIG. 14D is a graph of attained focus lengths of 1, 2 μm particles andbacteria at varying Re_(p) (a shorter device is used for the bacteriaexperiments to achieve higher Re_(p)).

FIG. 15A is a schematic of a “dog-bone” shaped microchannel(H_(narrow)=10 L_(narrow)=250 μm, H_(wide)=150 μm, L_(wide)=5.5 cm andW=64 μm) demonstrating oscillatory inertial focusing of 500 nm particlesin the microchannel.

FIG. 15B is a pair of fluorescent streak images (left) and correspondingFWHM graphs (right) showing oscillatory inertial focusing with 500 nmparticles.

Like reference symbols in the various drawings indicate like elements.

DETAILED DESCRIPTION

The current disclosure describes systems and methods that applyoscillatory (or “alternating current” (AC)) flow to inertial and/orviscoelastic focusing in small channels such as millimeter- andmicro-channels. These two passive particle manipulation modes are widelyused in microfluidics, albeit always in a steady flow (or “directcurrent” (DC)) configuration. For inertial focusing and viscoelasticfocusing, the present new systems and methods extend the residence timesof suspended particles to infinity, in theory (when the particles in afluid sample continue to move back and forth within a microfluidicchannel without moving from one location), essentially removing thepractical limits on channel length.

The new systems and methods directly push back the barriers to focusingsmall particles by orders of magnitude in pressure drop, shear stress,and ease of fabrication. In particular, given the ability to focussmaller particles more easily using inertial and/or viscoelastic forces,the new systems and methods enable expansion of inertial andviscoelastic microfluidic technology into manipulation of bacteria andeven viruses, while at the same time improving the tolerability of theprocess by larger, but especially sensitive, cells that might currentlysuffer damage during transit, such as mammalian cells.

The new systems and methods can be used for concentrating very smallparticles or cells (such as bacteria, yeast, exosomes, nanoparticles, orviruses), using very short and small channels (such as nanofluidicsystems), and very small driving pressures. They also widen the types ofmammalian cells that tolerate inertial and viscoelastic focusing due tosubstantially reduced shear stresses. Moreover, all of the standardapplications for inertial or viscoelastic focusing would incur benefits.These applications include sorting, separation, concentration,sheathless flow cytometry, controlled encapsulation by inertialordering, etc. Within the biotech industry, inertial and viscoelasticfocusing could also be combined with on-chip assays due to the dramaticshrinking of the required footprint and ability to increase residencetimes on-chip nearly without bound (including assays on cellularresponses to shear stress, controlled addition/removal of chemicals tocells, etc.).

General Methodology

Using oscillatory microfluidics, inertial focusing in practicallyinfinite channels can be achieved, allowing for particle focusing at themicron-scale and even smaller. Unlike traditional steady-flowmicrofluidics, oscillatory microfluidics switches the direction of theflow at a frequency high enough to avoid cells and particles travelingfurther than the whole device in a single step, but low enough thatcells or particles spend sufficient time in a fully-developed flowregime where focusing occurs and is understood.

Due to the symmetry of the velocity field along the flow axis, theinertial lift forces acting on the particle preserve theirdirectionality when the flow direction is switched (FIG. 1A). Byexploiting this symmetry, the focusing length can be extendedindefinitely, even though the channel itself has a short, fixed length.This method enables manipulation and focusing of small particles atextremely low particle Reynolds number (Re_(p)<<0.1) flows, which areotherwise unattainable by inertial microfluidics. In addition, shorterchannel length decreases the input pressure, which is a practicallimiting factor that can cause the device features to deform or break.Operation at extremely low Re_(p) regime also enables lower flowvelocities in channels with larger cross-sections, which reduces theshear stress experienced by the particles in the channel, allowing cellfocusing at physiological conditions.

A general schematic of an oscillatory microfluidic system that can beused to carry out inertial or viscoelastic focusing of particles intoone or more streamlines within a fluid sample is shown in FIG. 1B. Thesystem includes a fluid oscillator for alternating a direction of flowof the fluid sample through the microchannel, e.g., a symmetric orasymmetric microchannel; and a controller that transmits control signalsto the fluid oscillator to control the flow of the fluid sample in themicrochannel to be in a first direction at a set flow rate, to changethe first direction of flow to a second direction of flow opposite tothe first direction of flow and at a set flow rate, and to oscillate thedirection of flow between the first direction of flow and the seconddirection of flow at a set frequency and for a set period of time,thereby focusing the particles within one or more streamlines within thefluid sample flowing within the microfluidic channel.

In specific examples, the systems can include a pressure source, such asa pump, which can be a constant or varying pressure source, and a signal(pulse) generator, a valve driving circuit, and two high-speed valves,such as three-way valves (FIG. 1B).

As shown in FIG. 1B, a constant pressure source, e.g., 0-25 psi, can beconnected to 3-way valves at opposite ends of a microfluidic channel,e.g., made of polydimethylsiloxane (PDMS) or other plastics, metal,ceramic, or glass. The fluid sample and other liquids travel throughconduits to and from the microfluidic channel through plastic tubing,e.g., made of Tygon®. The pulse generator, e.g., 1 to 20 Hz, controlsthe valves via valve control 1 and 2 according to the source signal(valve 1) or inverted signal (valve 2) to provide the oscillatory flowwithin the microfluidic channel. Output and/or waste of the system(sink) is not pressurized in the depicted configuration, but can be ifdesired. Imaging is done in the imaging area shown in FIG. 1B.

As shown in the Examples below, inertial focusing can be achieved atRe_(p) at least as low as 0.005 when using the oscillatory flow methodsdescribed herein, about 20 times lower than previously attained, andsynthetic particles as small as 500 nm can be focused.

In summary, oscillatory inertial microfluidics achieves inertialparticle manipulation and focusing in a previously inaccessible flowregime, specifically at a very low Re_(p) range (Re_(p)<0.01) andparticle-to-channel ratios (a/H<0.1). We demonstrated this by inertiallyfocusing a variety of particles—as small as 500 nm—in oscillatory flows,including a bacterium (Staphylococcus aureus) in an 80 μm widemicrochannel using 20 psi driving pressure, which corresponded toRep=0.0047 and a/H=0.01. After demonstration of the method, we describedthe key principles for the design and operation of microfluidic devicesat this flow regime, based on experimental observations and anon-dimensional analysis of inertial migration.

The new systems can enable a new generation of inertial microfluidicdevices, which are unfeasible to implement using traditional, steadyflow microfluidics. While an analytical system was used in this study tobe able to investigate a wide range of parameters (in terms of particlesize, particle-to-channel ratio, and the dimensionless parameter Rep),purpose-built systems would be required to evaluate the performance ofthe proposed method for specific applications. These applicationsinclude inertial manipulation of smaller bioparticles such as bacteria,for the development of isolation devices based on label-free sorting ofthe pathogens. Larger bioparticles such as nucleated cells (e.g.,circulating tumor cells, white blood cells) can be sorted atphysiological shear stresses to ensure that the cells are not damaged orexhibit any flow-induced response, and also be repeatedly imaged ontheir focus plane while rotating for biophysical characterization orhigh sensitivity flow cytometry applications. We also expect that thevery low particle-to-channel ratio can potentially extend thecapabilities of inertial microfluidics to allow the use ofeasy-to-manufacture, millimeter-scale devices (e.g., manufactured via 3Dprinting) for cell and bioparticle processing, also at much lower shearstress.

Theoretical Background

Physics of inertial microfluidics, i.e., the forces that cause thelateral migration and eventual focusing of particles in microchannelsare well studied. The major practical challenge for inertialmicrofluidics in very low Re_(p) flows is the extensive channel lengthsrequired to attain focusing. To see this, consider first that themigration velocity of the particle due to inertial lift (U_(P)) can becalculated for a point particle as (assuming that the Stokes drag isbalancing the inertial lift force):

U _(P) =f _(L) ρU _(m) ² a ³/3πμH ²  [1]

where f_(L) is a dimensionless lift coefficient, ρ is the density of thecarrier fluid, U_(m) is the mean flow velocity in the channel, a is theparticle diameter, μ is the viscosity of the carrier fluid and H is thecross-sectional channel dimension of interest. Di Carlo has calculatedan estimated theoretical length which is required for inertial focusing,based on the U_(P) and the lateral migration length (of order H), forfinite particles. Adapting the same method to point particles usingequation [1], a similar expression can be obtained for the requiredchannel length for focusing (L_(f)) as:

L _(f,theoretical) =πμH ³ /f _(L) ρU _(m) a ³  [2]

From this relationship, it is apparent that the required length isinversely correlated with U_(m) and a³ (compared to U_(m) and a² forfinite particles). Regardless of the point or finite particleassumption, the required length and the pressure requirement of thesystem increases drastically with decreasing Re_(p), making itimpractical.

In a straight channel with rectangular cross-section (i.e., no Deanflow), a particle is subjected to two inertial lift forces (F_(L)): walllift force (F_(W)) and shear gradient force (F_(SG)) (see FIG. 1A)(DiCarlo, Lab Chip, 9(21):3038-3046, 2009). The combination of these forcesis often represented by: F_(L)=f_(L)ρU_(m) ²a^(x)/H^(y), where f_(L) isa dimensionless lift coefficient (which has a typical range of0.02-0.05), ρ is the density of the carrier fluid, U_(m) is the meanflow velocity in the channel, a is the particle diameter and H is thechannel dimension of interest (width or height). If a point particleassumption is made (i.e., particle does not disturb the flow, a<<H),then the exponents of a and H are found to be: x=4 and y=2 for theentire channel (Matas et al., J. Fluid Mech., 515:171-195, 2004, andAsmolov, J. Fluid Mech., 381:63-87, 1999).

More recent experimental measurements with finite particles(0.05<a/H<0.2) revealed that based on the lateral position of theparticle in the channel, a better fit for F_(L) can be obtained using:x=3 and y=1 near channel centerline, and x=6 and y=4 near the wallregion (Di Carlo et al., Phys. Rev. Lett., 102(9):1-4, 2009).Nonetheless, for both point and finite particle assumptions, F_(L) isstrongly correlated with the particle size (a) and flow velocity(U_(m)). Particle Reynolds number (Re_(p)) is a dimensionless numberconventionally used to characterize inertial microfluidic systems, whichencompasses both a and U_(m): Re_(p)=ρU_(m)a²/(μD_(h)), where μ is theviscosity of the carrier fluid and D_(h) is the hydraulic diameter ofthe (rectangular) channel: D_(h)=2WH/(W+H), where W is thecross-sectional dimension other than H.

Based on the dimensionless number regimes such as the channel Reynoldsnumber (Re or Re_(ch)), particle Reynolds number (Re_(p)), or the ratioof particle diameter a to the hydraulic diameter of a microchannel D_(h)(a/D_(h)), we can define the frequency and also the travel distances ina given system. The frequency of the oscillations is limited in thelower end by the distance they travel. In particular, the traveldistance should not exceed the total length of the microfluidic channelin the microchip. Thus, the frequency and travel distance is correlated.In the higher end, the oscillation frequency is limited by the entrancelength (the length required for the flow to develop). For laminar flow,this is quantified by the standard dimensionless Womersley number (Wo):

Wo=D _(h)(2*π*f*ρ/μ)^(1/2)

where D_(h) is the hydraulic diameter, f is frequency (Hz), ρ isdensity, and μ is dynamic viscosity. Small Wo (<1.0), e.g., 0.1, 0.2,0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, or 0.95 means entrance length effectscan be ignored, which means the flow is fully developed for almost allof the oscillation.

In general, the streamline positions achieved by the new oscillatoryflow methods are the same as for steady flows. For example, in squarechannels, the particles will follow four streamlines, one centered alongeach of the four walls. In rectangular channels, one obtains twostreamlines, one along each of the long walls, centered on that wall. Ininertial fractionator systems, which can be systems with square orrectangular channels, the separation results in displacement from onechannel to another.

In curving channels, there will be two streamlines along the centeroffset (2 on top of each other). For example, the disclosure includesmethods for focusing particles in a moving fluid by providing particlessuspended in a moving fluid into a channel, wherein the channel iscurved and has a rectangular cross-section, a height, a width, and ahydraulic diameter equal to 2*height*width/(width+height); and flowingthe fluid through the channel under conditions such that inertial forcesacting on the particles result in the localization of a flux ofparticles in the channel, wherein a lift/drag ratio for the particles isgreater or equal to one over a limited region of the channel crosssection and the magnitude of the forces is large enough to createfocusing of the flux of particles to one or more streams that arelocalized to within an area having a width of, at most, five times thewidth of the particles in one dimension.

For discussions of inertial focusing, see, e.g., U.S. Pat. Nos.9,808,803; 9,895,694; and 9,610,582; and US Published Patent ApplicationNo. US2016/0123858. All of these references are incorporated herein byreference in their entireties, including their figures and claims.

Viscoelastic focusing results in focusing to corner positions and centerstreams in square/rectangular channels, and the center stream isdisplaced from the centerline as a function of curvature in curvingchannels. The corner positions may not be present when particles are toobig to fit. Viscoelastic effects exist when the Weissenberg number isgreater than zero (Wi=λU/H, where λ is characteristic relaxation time, Uis mean channel velocity, and H is the narrowest channel dimension). Ina square channel, the focusing positions include the channel centerlineand close to the four corners, however, as particle size increases onlythe center stream is accessible. The time required to focus particlesdoes depend on particle diameter, but for oscillatory flow, a need forlong duration of flow does not prevent successful focusing. Therefore,successful focusing is possible by viscoelastic effects when Weissenbergnumber is greater than zero.

The elasticity number, defined as El=Wi/Re, allows the relative effectsof viscoelastic and inertial focusing fluid forces to be compared. WhenEl<<1, inertial focusing dominates, along with the characteristic focuspositions, but when El>>1, viscoelastic focusing dominates, revealingseparate focus positions. When El˜1, inertia-elastic focusing occurs,whereby the focus positions of particles are modified rather thanswitching from one set to the other set. For example, the cornerpositions that are often present in viscoelastic focusing can beeliminated, while the center focus position remains precisely focused.This can persist to quite high Reynolds numbers, even exceeding thetextbook limit for onset of turbulence.

For discussions of viscoelastic focusing, see, e.g. US Published PatentApplication No. 2016/0339434; Lim et al., “Inertio-elastic focusing ofbioparticles in microchannels at high throughput,” NatureCommunications, 5:4120 (2014); and Seo et al., “Lateral migration andfocusing of microspheres in a microchannel flow of viscoelastic fluids,”Physics of Fluids, 26:063301 (2014). All of these references areincorporated herein by reference in their entireties, including thefigures and claims.

Oscillatory Inertial Focusing Systems

FIG. 2 shows a schematic of a microchip and several inputs and outputsalong with a controlled pressure or controlled flow source used in amethod in which the input pressure or flow is controlled to oscillate.In this method, a system creates flow fields on the microchip bycontrolling the pressure or flow sources. If a pressure source is used,the outlet pressure of all the pressure sources can (i) alternatebetween a high and low state at a set frequency, (ii) transition betweena high and low state in a gradual manner (similar to a sine wave), or(iii) have a predefined profile which will change the pressurization ofa fluid in a container. Based on the combination of these pressureprofiles from n different pressure sources, oscillation of the fluid inthe microchip is achieved. If a flow source is used, the flow-rate can(i) alternate between a high and low state at a set frequency, (ii)transition between a high and low state in a gradual manner (similar toa sine wave), or (iii) have a predefined profile which will result in aset flow-rate (net in, net out, or zero) of the fluid container. Thecombination of the pressure of flow-rate profiles will be used tooscillate the flow field in the entirety or only part of themicrofluidic channel, continuously or intermittently, with or without anet resulting flow. Any n number of pressure or flow sources can be usedin combination to achieve the desired flow field on the microchip.

FIG. 3 shows a system and method similar to that shown in FIG. 2, but inthis method the input pressure or flow is controlled to be steady andvalves and/or fluidic resistance and/or capacitance components arecontrolled to oscillate the flow. In this method, a system creates flowfields on the microchip by controlling valves or other fluidic controlcomponents between pressure or flow driven fluid samples and themicrochip. Valves can be three-way valves, on-off valves, or other fluidcontrol components that can be externally controlled via an electrical,hydraulic, pneumatic, or other signal. In addition to valves,transient-response fluidic components such as a combination of fluidicresistances and fluidic capacitances can be used to obtain a set timedependent response of the fluid flow. Resistances can be created by longtubing with small hydraulic diameters. Capacitances can be created byelastic tubing components that will swell with pressure, fluidreservoirs with a preset capacity that will fill until a limit, or othermethods. Any n number of steady or transient fluid flow controlcomponents will be used to oscillate the flow field in the entirety oronly part of the microfluidic channel, continuously or intermittently,with or without a net resulting flow.

FIG. 4 shows a system and method similar to that shown in FIGS. 2 and 3,but in this method the input pressure or flow is controlled to be steadyand valves and/or fluidic resistance and/or capacitance componentsintegrated on the microchip are controlled to oscillate the flow. Inthis method, a system creates flow fields on the microchip bycontrolling microfluidic valves or other fluidic components integratedon a microchip, e.g., a PDMS microchip. Microfluidic valves can bethree-way valves, on-off valves, or other fluid control components thatcan be externally controlled via an electrical, hydraulic, pneumatic, orother signal. Some of these on-chip valves rely on the deformation ofPDMS layers under pressure, such as the quake valves developed atStanford (see, e.g., Unger et al, “Monolithic Microfabricated Valves andPumps by Multilayer Soft Lithography,” Science, 288(7):113-116, April2000).

Instead of on-chip valves, transient fluidic components such as fluidicresistances and capacitances can be used to obtain a set time dependentresponse of the fluid flow. Resistances on the microchip are created bylong channels with small hydraulic diameters. Capacitances on themicrochip can be created by a large deformable section that will swellwith pressure, or introducing a bubble of vapor, gas, or a mixture ofgases (such as air) that will enlarge or shrink with pressure. Any nnumber of steady or transient on chip fluid flow control components willbe used to oscillate the flow field in the entirety or only part of themicrofluidic channel, continuously or intermittently, with or without anet resulting flow.

Any one or more of the control mechanisms outlined in FIGS. 2-4 can becombined with each other and in general, description of one method ofcontrolling the oscillatory flow does not preclude the ability tocombine it with one or more other described modes of flow actuation(such as reciprocating machinery).

System Throughput

In an oscillatory inertial microfluidics system, the physical length ofthe channel is shorter (with respect to traditional steady flow) and isvirtually extended by making the particles spend more time in thechannel. This, in turn, reduces the throughput per channelproportionally with the extended time. For instance, if the inertialfocusing length is extended an order of magnitude via oscillatory flow,it is expected that the throughput of the system will decrease an orderof magnitude, if no other changes are made to the system.

We propose that this reduction in the single channel throughput can bealleviated by increased parallelization of the channels. Due to theshorter channel length, it is possible to fit more devices in the sameoverall footprint, which enhances parallelization and scaling. Forinstance, if the inertial focusing length is extended ten-fold viaoscillatory flow, ten times the number of channels could be fitted inthe same geometry instead of an equivalent, ten-fold longer channel. Inaddition, in the oscillatory case, the pressure drop would besignificantly less due to the shorter channel length. It should be notedthat while the higher parallelization would bring additional engineeringdesign challenges, the feasibility of highly parallelized microfluidicchips on injection-molded plastic devices has been successfullydemonstrated (see, e.g., Lim et al., Nature Communications 5, 4120(2014) and Fachin et al., Scientific Reports, 7(1), 10936, 2017).

Applications of Oscillatory Inertial Focusing

The new oscillatory inertial focusing techniques can be used in avariety of existing inertial focusing systems and for a variety oftasks.

Concentration by Pressure Control and Forward Flow Bias

FIGS. 5A to 5E relate to systems and methods to concentrate particles ina fluid sample. Focusing of particles into specific streamlines can beused to concentrate focused particles when those streamlines are sortedinto a “product” outlet in a fluidic circuit by means of controlledoutput flows. For example, a straight channel or “dog-bone” separator(FIG. 5A) operates by first oscillating the flow to induce focusing ofparticles within the narrow region. For inertial focusing where thenarrow channel is taller than it is wide, this will result in focusingof particles into two streamlines near the sidewalls and mid-height ofthe channel (side focusing). The focused particles can then be extractedas pictured by removing the center streamlines as waste.

For inertial focusing where the narrow channel is wider than it is tall,this will result in focusing of particles into two streamlines along themiddle of the channel, but displaced above and below the mid-height ofthe channel (center focusing). Separation is then accomplished by takingthe center streamlines as a product fraction, which retains the focusedparticles. For viscoelastic focusing, particles migrate to thegeometrical center and, depending on the flow conditions, to the cornersof the narrow channel (see, e.g., US Published Application No.US2016-0339434). In either case, the product is now in a much smallervolume of sample liquid, and is thus concentrated.

In straight, uncurved channels (no Dean flow), the inertial focusingwill result in two or four streamlines in two positions (along thelonger sides of the microchannel) if the channel where focusing ishappening is more rectangular. Four streamline positions, again near thesidewalls, will result if the channel is closer to a square than arectangle. The expected streamline positions within a straightmicrochannel, and how to determine them, are known to those of skill inthe field of inertial focusing, as described, for example, in U.S. Pat.No. 9,808,803.

Besides, a simple straight channel, other steady-flow devices that takeadvantage of inertial focusing (or viscoelastic focusing) can beutilized in an oscillatory mode, provided that the oscillation frequencyis high enough to avoid particles traveling too far (e.g., from thebeginning of one separation element through a point where separationoccurs in a single forward step). For example, the inertial concentratorshown in FIG. 5B excludes particles above a size cutoff from thestreamlines nearest the inner wall of the tight curve, then siphons awaythat fluid bit by bit even as particles continue to be pushed from thatnear wall in subsequent concentration units. Oscillatory flow willincrease the migration distance away from the inner wall of the tightturn because it provides a longer effective travel distance. Therefore,more of the flow can be siphoned after each separation island, allowinga shorter overall device and lower pressure drop for a fixedconcentration factor. Alternatively, slower flow can still achieveconcentration, reducing the shear stresses experienced, particularlyuseful for concentration of biological cells.

In the embodiment of FIG. 5B the curves and forward flow rates cause theparticles (product) to focus into one streamline along a sidewall. Theparticles in the product streamline are thus concentrated in a muchsmaller volume of the sample liquid, as the rest of the sample liquid isremoved as waste. Note that a curved geometry such as shown in FIG. 5Bwill have one streamline because of the additional Dean flow. See, forexample, U.S. Pat. No. 9,808,803.

To take advantage of the alternating flow control, one usefulimplementation involves three controlled pressure ports, one for sample,product, and waste (FIGS. 5C and 5D). By oscillating the pressures suchthat sample pressure is high when the waste and product pressures arelow, and vice versa, the focusing length can be sufficient even within ashort narrow section for effective separation. In this embodiment, thehigh and low pressures are kept constant between the forward and reversephases of operation, but more time is spent in the forward flow step asshown in the graph of FIG. 5E. This results in a forward bias such thatseparation would take place without need of further intervention.

Separation by Pressure Control and Forward Flow Bias

Besides concentration of focused particles, oscillatory flow can also beapplied to displace focused particles out of a first fluid and into asecond fluid. To accomplish this, the second fluid is most oftenintroduced into a co-flowing set of streamlines (buffer), adjacent tothe flow of streamlines containing the input particles (sample). Foroscillatory flow, the buffer pressure could then be synchronized to thesample inlet pressure in both the forward and reverse phases, leavingthe product and waste pressures synchronized to each other, yet reversedfrom the buffer and sample reservoir pressures (the simplestimplementation).

As shown in FIG. 6A, a first example is given, whereby an array ofislands progressively separates particles that, through inertialfocusing forces, are excluded from the near-wall region from which fluidstreamlines are siphoned back. In steady flow, sufficient migration awayfrom the wall must occur only within the length of each island in orderfor the desired particles to be ultimately displaced into the productlane of the separation device. Taking the simplest form of oscillatoryflow control (pressure oscillation from a high to low pressure, withmore time spent in the forward phase), the migration distance away fromthe near wall is no longer limited by the length of the island, sincethe particle can travel many times the length of the island according tothe oscillation frequency and velocity within the particle streamline.Therefore, the fraction of flow siphoned at each break between islandscan be increased, resulting in an overall shorter device with reducedpressure drop.

Alternatively, the flow speed can be reduced with the same siphoningfraction applied during steady flow, reducing the shear stressexperienced by, for example, biological cells. In this implementation,the travel distance of the particle in the (longer) forward phase shouldnot exceed the length of an island plus the gap distance from one islandto the next, otherwise the particles can find themselves in the siphonedstreamlines where they will migrate away from the back-wall of thesubsequent island, preventing them from reaching the product stream.

Alternatively, as shown in FIG. 6B, inertial focusing in a spiral device(with co-flow) can be augmented in a similar fashion. One added benefithowever for oscillatory flow in spirals arises from the limitation understeady-flow: the radius of curvature must gradually change from inlet tooutlet to prevent channels from merging from one turn to the next. Inoscillatory flow, the range of channel radius can be greatly reduced (oreven eliminated if the curving channel is less than a full revolution).This can be utilized to study the inertial focusing process in spiralsbesides all of the benefits to reduced pressure drops and shear stressesthat are incurred in the other implementations of oscillatory flow toinertial focusing-based separations.

These two systems are shown schematically in FIGS. 6C and 6D, in whichthe inputs (buffer and sample) and outputs (waste and product) are shownin the forward flow (6C) and reverse flow (6D). The reservoir pressuresover time are shown in the graph of FIG. 6E.

These separation devices can also be applied with viscoelastic focusingin an analogous manner with how the straight-channel separator(“dog-bone”) format could be adapted for viscoelastic focusing. Only thepositions of the focus streams change and flow parameters needed toachieve focusing of particles out of the waste streamlines.

Intermittent Flow

Besides oscillatory flow where the inlet and outlet reservoirs aredriven with an oscillatory pressure continuously, intermittent modes ofoperation are also useful, as shown schematically in FIGS. 7A and 7B.For example, in a concentration focusing chip module, a period offocusing can occur indefinitely in Phase 1 by matching the time andpressure spent in the forward and reverse modes (zero net flow), asshown in FIG. 7A and in particular the graph of oscillating reservoirpressure over time. As shown in FIG. 7B, in Phase 2, concentration canthen occur during a specified time spent in the forward phase of flow(see the graph of steady pressure in the reservoirs over time). Thiswould be designed to push the focused particles nearest the separationpoint all the way beyond a point where no oscillation occurs, therebyachieving separation. This method could be applied also to situationswith a second fluid into which particles become displaced.

Intermittent Flow for Water Filtration

One application for enhanced inertial focusing by oscillatory flow is inprolonging the life of filters for water purification or other fluidfiltration. In this implementation, particles caught by the filterduring a dispensing mode would be removed quickly from the filter poresby AC inertial lift forces away from the wall, then shuttled to a nearbywaste port. Because this cleaning step could occur often (perhaps everyminute or less), particulates would have little chance to formnonspecific adhesions to the filter before cleaning, yet because thecleaning step could utilize only a tiny volume of water, essentially allthe water would proceed on into the product with just a tiny volumeexcreted as waste. There would also be no need for an additive as in thecase of viscoelastic focusing. This particular application could finduse in consumer refrigerators, attachments to faucets, and even handheldwater purification kits. Any type of filter, e.g., flat filters andhollow fiber filters, can be modified (e.g., to alter the flow patternsand to include a waste port if not already present) using the newsystems and methods. It is worth pointing out that this would beimpossible without the dramatic reduction in pressure drop afforded byAC inertial focusing.

In one embodiment of water filtration shown in FIGS. 8A and 8B,intermittent oscillatory flow is used to clean particles from a filter.As shown in FIG. 8A, a filter can be cleansed intermittently in Phase 1by oscillating the direction of flow between the sample input (dirtywater in this case) and the product output (clean water)(see the graphof FIG. 8C). When a focusing element exists on the upstream side of thefilter, the filtrate can thus be concentrated into a set of focusstreamlines based on the geometry of the focusing channel, and thesestreamlines can then be removed into a waste output by operating thedevice as a concentrator, whereby a steady flow from sample is driven tothe product and waste outlets such that the focused stream of filtrateexits into the waste port rather than being reintroduced to the filterpores. The primary benefit of using an intermittent mode for filtrationis that the filter pores can effectively concentrate the filtrate from alarge sample volume into a small on-chip volume of filtrate that iseasily focused with a low to zero net flow before concentrating it tothe waste.

As shown in FIG. 8B, in Phase 2, the loose particles are removed fromthe system using a brief forward flow to separate the filtrate and causeit to pass out through one or more waste ports (see FIG. 8D, whichschematically shows a water filter in each of Phases 0, 1, and 2). Thedirty water to be filtered is then passed through the filter with asteady flow in the forward direction (Phase 0). In FIG. 8D, the waterfilter has an inlet and one or more waste outlets (two shown) and thesmall angular islands represent any filter material, though the currentmethods would work best on shallow filters and hollow fiber filters,i.e., not filters that include a packed bed of particles, becauseparticles trapped deep within a porous filter may have a hard timeexiting back upstream for removal post-focusing.

In another embodiment of the filtration application, the inertial fluidforces that cause particles to migrate away from walls can be used todislodge and then displace particles that have been filtered. Thisperforms oscillation between the sample and waste while the product isclosed, then displaces the focused filtrate all to the waste beforereturning to a steady flow operation from sample to product to filterthe sample until the filter needs cleaning again. The advantage is thereis no need for a backflow through the filter.

Intermittent Flow for Cell Lysis

This application uses the same configuration as the water filtrationscheme described in FIGS. 8A-C, but without Phase 0. The system normallyoperates at Phase 1 shown in FIG. 8A, and cells are focused into definedstreamlines with known shear stresses based on their distance from thewall. By setting the shear stress sufficiently high (e.g., via increasedpressure, in a pressure driven system), the cells are lysed because ofthe prolonged periods of shear stress exposure during oscillation. Asthe cells are being lysed, the sample is also driven through the filterof the configuration shown in FIG. 8D with a forward bias in the netflow, where the contents of the cells (product) pass, but the celldebris is caught by the filter. Thus, the intracellular contents will becollected after the filter without the cell debris. Then, via Phase 2depicted in FIG. 8B, the cell debris (waste) will be removed from thefilter via side channels if necessary. Note that if the shear stress isnot high enough to lyse the cells, the system works simply as a waterfilter.

Though the aforementioned configuration utilizes a filter, note that ifconcentration by the filter is not needed, a single inlet single outletoscillatory flow setup such as in FIGS. 9A-C (described in furtherdetail below) would enable a continuous lysis of input cell suspensionat predictable shear rates. Because the residence time is decoupled fromthe shear stress due to oscillation, this can enable fine tuning of celllysis, perhaps at lower shear rates than required by steady flow,resulting in potentially less fragmentation of nucleic acids that arereleased during the process, or potentially more as desired by extendedtime of shearing.

Long Duration Cytometry at a Controlled Shear Rate Streamline

One implementation of oscillatory flow to focus particles (by inertialor viscoelastic fluid forces) does not require separation, and that iscell cytometry. For example, focusing of cells into defined streamlinesnear the walls of the narrow channel will achieve known shear stressesin similar fashion to a cone and plate viscometer or cylinder and drumviscometer, because the cells will be a defined distance from the wall.This can be used to observe the changes to cells under prolonged periodsof defined shear stress in the oscillatory mode. This can also be usedto observe breaking of individual cell clusters as a means of assayingcell-cell binding strengths.

Alternatively, prolonged imaging of particles from multiple angles underoscillatory flow can enable a 3D reconstruction of their structure, withimages being obtained by high-speed video or fluorescence (includinglaser-scanning confocal imaging) with periodic stops in the flow to holdthe particle motionless for a short time. As shown in FIGS. 9A and 9B,this type of setup can operate with a single input and output and zeronet flow (see the graph of FIG. 9D) during the focusing and imagingphase. When a new set of particles is desired to observe, the flow canbe put into a forward phase until new particles enter the focusingchannels (FIG. 9A). By using an architecture where feeder channels aremuch taller than the focusing channels, a large number of focusingchannels could be arrayed in parallel while still being certain of theapplied flow speed being relatively consistent throughout all of thefocusing channels. This arrangement is shown schematically in FIG. 9C.

Reciprocating Motion to Achieve High RPM Oscillatory Flow

Although the simplest form of driving an oscillatory flow is either bycontrolling the pressure within the input and output fluid reservoirsdirectly or by switching the input streams between reservoirs atdifferent pressures through valving, additional means of drivingoscillatory flows exist. For example, as shown in FIG. 10B,reciprocating devices such as piston-cylinders driven by rotatingmachinery, are very effective at driving large changes in pressure athigh frequencies with great precision. As depicted, an array of fluidreservoirs could be controlled by adjusting the compression ratio (finalvolume over initial volume in the cylinder), the revolutions per minute,and even the mass of air or gas above the fluid inside the cylinder. Theadvantage for such methods for pressure control is that they can drivevery rapid changes in pressure through simple means; however, thepressure profiles are no longer square waves. Effective separationdevices would certainly be possible with sinusoidal pressure controlwith appropriate accounting for the particle migration speeds at eachintermediate pressure. Such sinusoidal pressure control over time isshown in the schematic graph of FIG. 10A.

EXAMPLES

The new systems and methods are further described in the followingexamples, which do not limit the scope of the invention described in theclaims. The following Materials and Methods were used for all of theExamples.

Materials and Methods

Monodisperse fluorescent polystyrene particles (Fluoro-Max, SigmaAldrich, USA) and bacteria (SH1000-GFP Staphylococcus aureus strain,which expresses green fluorescent protein) were diluted in PBS solutionsand density matched by adding Optiprep® (Sigma Aldrich, USA). Stocksolutions of particles were received at 1% wt/vol concentration, andtheir final concentration (after dilution) ranged from 0.02% to 0.001%wt/vol based on the particle size.

Bacteria were harvested at 1.7×10⁹ cells/mL concentration, and werediluted 100-fold before being used in the experiments. An aircompressor, which can deliver up to 25 psi pressure, was used to drivethe flow. The high-speed three-way solenoid valves (LHDA0533315H) wereobtained from The Lee Company (CT, USA).

PDMS devices were fabricated using standard soft lithography techniques(30). Microfluidic devices used with larger (a=3, 4.8 and 10 μm)particles had a width (11) of 80 μm and a length (L) of 4.3 cm, anddevices used with smaller (a=1, 2 μm) particles had H=40 μm and L=6.2cm, and the device used with bacteria (a=0.8 μm) had H=80 μm and L=2 cm.Prototype dog-bone microfluidic device had a narrow section with: H=10μm and L=250 μm, and an expansion section with: H=150 μm and L=5.5 cm.All channels had a fixed depth: W=25±3 μm, except for the dog-bonedevice which had: W=64±2 μm.

The components of the system were connected to each other via Tygon®Tubing (Cole Parmer, USA). A monochrome Retiga® 2000R camera (Qimaging,BC, Canada) was used to record streak images of the particles. Inertialmigration video of an individual particle was obtained by recording witha high-speed camera (Phantom 4.2, Vision Research Inc.) at a framecapture rate (10 fps) that matches oscillation frequency of the flow (10Hz). Therefore, the particle appears to have minimal horizontalmovement, despite travelling outside the field of view and coming backin an oscillation cycle.

Example 1—Inertial Focusing in Oscillatory Flow

We demonstrated the inertial focusing of the particles in an oscillatoryflow system by monitoring the particles over time at a fixed location ina straight microchannel. The system consists of a pressure source, asignal (pulse) generator, a valve driving circuit and two high-speedthree-way valves (FIG. 1B). The valves are driven by two rectangularsignals, where one of the signals is the inverse of the control signalso that the microfluidic circuit is completed in one direction or itsreverse. The net flow in the microchannel is adjusted by the duty cycleof the control signal, where 50% corresponds to zero net flow, and anybias towards 0% or 100% duty cycle correspond to a net flow in eitherdirection. In our experiments, since we were monitoring the inertialmigration of the same set of particles at a fixed location in themicrochannel, we operated the system at zero net flow to be able measurethe focusing time of the particles.

Using the system of FIG. 1B, we were able to track an individualparticle as it inertially migrates towards the center of the channel(see Materials and Methods for details) while oscillating (i.e., leavingand re-entering the field of view). However, for characterization of theinertial focusing behavior, we used fluorescence streak imaging with agroup of particles (FIG. 11A). The preferred inertial focusing positionat the center of the channel resulted in a sharp intensity peakformation over time (FIG. 11B). The focus time (t_(f))—the time wheninertial focusing was achieved—was evaluated using full-width athalf-maximum (FWHM) analysis using the streak images (FIG. 11C).Specifically, t_(f) was determined as the time point where FWHM reachedits stable minimum. In this specific case, the focus time (t_(f)) andlength (L_(f)) were determined as 48 s and 5.7 m respectively,corresponding to two orders of magnitude enhancement to the physicalchannel length (˜0.04 m).

Note that experimental determination of L_(f) in an oscillatory flowrequires measurement of particles' travel length. For streak imaging,this requires very dilute particle solutions and the oscillatory travelpath of the particles to be restricted to the imaged area of themicrochannel, which is impractical at low oscillation frequencies. Dueto these complications, we opted to calculate L_(f) based on the meanflow velocity using: L_(f)=t_(f)U_(m), where t_(f) is the experimentallydetermined focus time.

Upon validation of the oscillatory inertial focusing, the system wasfurther tested with 3.1, 4.8 and 10 μm particles at varying flowvelocities. The flow velocity in the microchannel was adjusted byvarying the driving pressure from 1 psi to 25 psi. To keep the Re_(p)within a comparable range for different size particles, the testedpressure range was decreased as the particle size increased. This alsoensured that when the particles were introduced to the channel, therewas no inertial focusing and particles were randomly distributed. Theinvestigated frequency range for each particle size/pressure pair wasselected based on the calculated mean velocity of the particles at agiven pressure (P), focusing time (t_(f)) of the particles, and theresponse time of the microfluidic valves. Specifically, the minimumfrequency was set to ensure that the particles stayed in the channelduring their oscillatory travel. Thus, for instance, at high pressures(i.e., high U_(m)), lower frequencies were not tested as the particleswould have to leave the channel. The maximum frequency (f=20 Hz) was setto ensure that the response time of the valve (˜5 ms) was small comparedto the period of oscillation, however high speed valves in the kHz rangeare available commercially.

A trend between increased Re_(p) and decreased focus time (t_(f)) andfocus length (L_(f)) was observed, for a constant particle size (FIGS.12A and 12B). The fastest focusing (˜5 s) was achieved with 10 μmparticles at 5 psi driving pressure (Re_(p)=0.083), while the slowestfocusing (˜10 min) was achieved with 3.1 μm particles at the samepressure (Re_(p)=0.0068). As shown in FIG. 12A, note that while fasterfocusing could be attained for 10 μm particles using a higher pressure,we opted to limit the pressure to maintain the Re_(p) values comparableto the smaller particles and ensure that the particles were not focusedwhile entering the channel, as previously discussed. Thus, 5 psi was thehighest pressure selected for 10 μm particles and the lowest pressureselected for 3.1 μm particles.

Attained focus lengths (L_(f)) ranged approximately from 0.1 m up to 20m (FIG. 12B). The shortest L_(f) was achieved with the 10 μm particlesat 5 psi, while the longest L_(f) was achieved with the smallest (3.1μm) particles at 5 psi. For different size particles operating at asimilar Re_(p), L_(f) decreased with increasing a, which shows that aand L_(f) were explicitly correlated, beyond their implicit correlationvia Re_(p). For these set of experiments, the channel width (thedimension that the migration is observed, H) was 80 μm, thus a/H changedfrom 0.8 to 0.04, as the particle size got smaller. Therefore, we alsoconcluded that the finite particle assumption did not hold for theexplored particle size range.

Based on our data, we identified that inertial focusing in oscillatoryflow can occur at Re_(p) values as small as 0.002. Since Re_(p) and Reare correlated via (a/D_(h))², we identified a triangular parameterspace bound by Re, Re_(p), and a/D_(h) (see FIG. 13A). This space isbound on the upper end by Re≈2300 due to the laminar to turbulenttransition of the flow, though it should be noted that this limit isconservative since onset of turbulence can be pushed to much higherReynolds numbers with viscoelastic additives and/or smoother channelsidewalls for example. On the lower end, it is bound by our lowestexperimentally observed Re_(p) (0.002), and a/D_(h)<about 0.5-1.0, whichensures that particles are smaller than the smallest cross-sectionaldimension of the channel. We also experimentally observed thatoscillatory inertial focusing occurs at Womersley number (Wo) as largeas 2, e.g., 1.25, 1.5, or 1.75 (note that Wo determines whether entrancelength effects can be ignored), but Wo is typically less than 1.0. SinceWo is correlated to frequency (f) and D_(h), we also identified anoscillation frequency and D_(h) space that oscillatory inertialmicrofluidics would work (see FIG. 13B).

Example 2—Inertial Focusing of Micron to Submicron-Scale Particles inOscillatory Flow

A previously unexplored diffusion barrier on inertial focusing becameevident when focusing particles that are 2 μm or smaller. We observed nofocusing behavior with the 2 μm particles at the lowest tested pressure(Re_(p)=0.0025), even after the particles had travelled for extremelylong times and distances in the microchannel (10 min and 12.7 m,respectively) (FIG. 14A). Therefore, we concluded that at thiscritically low Re_(p) range, a diffusion limited no-inertial-focusingregion was present.

When the Re_(p) was increased to 0.0050, focusing was observed but thefocused streamline was uncharacteristically wide, as the systemtransitioned from diffusion dominated to inertially controlled regime.Only when the Re_(p) was increased beyond 0.0075, a typical, narrowlyfocused particle stream was observed. Using the same device with 1 μmparticles, focusing was observed only at the highest allowable pressure(Re_(p)=0.0031). The different regimes based on the focus quality (i.e.width of the attained particle stream) were also quantified using FWHMevolution plots (FIG. 14B).

In the diffusion limited particle size range, higher flow velocities arerequired to improve Re_(p) and focus quality, while maintaining theinertial focusing length in the order of meters. This is impracticalwith steady-flow due to the extreme pressure requirement, butoscillatory microfluidics allows virtually infinite lengths withoutincreasing the pressure, and the minimum physical channel length is onlylimited by the maximum frequency of the high-speed valves or otherpressure-controlling elements (e.g., rotating machinery or pressurecontrollers). We used a shorter and wider device to focus Staphylococcusaureus to compensate for the decrease in the Re_(p) due to the smallerparticle size (0.8 μm), thereby enabling operation at a higher Re_(p)(0.0047) than 1 μm particles without increasing the pressure.

Note that in this case, the channel dimension in which we observedparticle migration and focusing was 2 orders of magnitude larger thanthe particle size (a/H=0.01). Under these parameters, we observedinertial focusing of bacteria (FIG. 14C), and the focus quality wassimilar to the previous results at a comparable Re_(p) range. For thisset of experiments, the longest focus length (L_(f)=24.7±7.4 m) wasattained with 1 μm particles (FIG. 14D).

Example 3—Varying Cross-Section (Dog-Bone) Microchip Design

Based on our findings, we developed a prototype dog-bone shapedmicrofluidic chip for inertially focusing smaller (i.e. a few hundredsof nm) particles. Our previous results demonstrated that to achieve highquality inertial focusing, Re_(p) needs to be sufficiently high. Thus,the further decrease in the particle size needs to be compensated byincreased flow velocity. To achieve this, a varying cross-sectionmicrochip was designed with a very narrow and short section, where thesmall cross-sectional area and short length enables higher flowvelocity. The narrow section is connected to two wider sections of thechannel, where the pressure drop is reduced, and the decreased flowvelocity ensures that the particles are kept in the channel during theiroscillation. The resulting shape, similar to a “dog-bone,” is shown inFIG. 15A.

It was observed that at P=25 psi, 500 nm particles focused on the sidefocusing positions of the channel (FIG. 15B), as a result of thepreferred focusing positions shifting to the sides due to the high depthto width ratio (W/H=6.4) of the narrow section. Even though this ratiois less than unity in the expansion section (W/H=0.42), the inertiallift forces are also significantly weaker, thus the focusing positionsare determined by the geometry of the narrow section where focusingtakes place. Using this geometry, the corresponding flow parameters inthe narrow section of the channel were calculated as: Re_(p)=0.052; wellwithin the range where we were able to obtain focusing using straightchannels (FIG. 15B). Similar to those results, focusing was attained ina short time-scale (t_(f)=10 s).

Example 4—Low (Physiological) Shear Stress at Very Low Re_(p)

Operating at a very low Re_(p) range also enables particles that aresimilar to white blood cells in size (10 μm) to be inertially focused atvery low input pressures and larger channels, which translates to cellsbeing exposed to minimal, physiological-scale shear stress levels. Thisis desirable to ensure that cells remain unharmed and do not exhibit ashear-induced response, and also to avoid clogging and malfunction ofblood processing devices, due to shear stress activation of plateletsand von Willebrand factor (vWF) fibers (26, 27). The physiological shearstress levels in the veins and arteries are reported as 1-6 dynes/cm²and 10-70 dynes/cm², respectively.

We conducted a finite element simulation of a fully developed flow inour microchannel using COMSOL MULTIPHYSICS® computational fluid dynamicssoftware (COMSOL Inc., Burlington, Mass.). We applied the same flowconditions (applied pressure, fluid properties) where we previouslyobserved focusing of 10 μm particles (80 μm×25 μm cross-section). Notethat these particles are comparable to white blood cells, and smallerthan other clinically relevant nucleated cells (e.g. circulating tumorcells (CTCs).

We evaluated the maximum (on the channel wall), and the average shearstress as 18.4 dynes/cm² and 8.3 dynes/cm² respectively, which are bothin the physiological range. Because it gets easier to focus particleswith larger diameters, it is reasonable to assume that larger nucleatedcells such as CTCs or CTC clusters would be focused at even lower flowrates. Therefore, we concluded that white blood cells and largernucleated cells or clusters can be inertially focused under conditionsthat are similar to physiological conditions, therefore can be ensuredto not be harmed by the microfluidic process.

OTHER EMBODIMENTS

It is to be understood that while the invention has been described inconjunction with the detailed description thereof, the foregoingdescription is intended to illustrate and not limit the scope of theinvention, which is defined by the scope of the appended claims. Otheraspects, advantages, and modifications are within the scope of thefollowing claims.

1. An oscillatory fluidic system for focusing of particles in a fluidsample into one or more streamlines within a fluid flowing in a channel,the system comprising a fluid oscillator for alternating a direction offlow of the fluid in a channel; and a controller arranged and configuredto transmit control signals to the fluid oscillator to generate arepeating oscillating flow profile of the fluid sample in the channel,wherein the flow profile includes at least one step in a first directionof flow and at least one step in a second direction of flow opposite tothe first direction of flow, for a set period of time, thereby focusingthe particles into one or more streamlines within the fluid flowingwithin the channel.
 2. The system of claim 1, further comprising amillimeter or micrometer channel.
 3. The system of claim 2, wherein thedimensions of the channel and the controller are configured to provideinertial focusing.
 4. The system of claim 2, wherein the dimensions ofthe channel and the controller are configured to provide viscoelasticfocusing when a fluid in the channel is selected to have an appropriateviscoelasticity.
 5. The system of claim 1, wherein the fluid oscillatorcomprises a source of pressure or flow arranged and controlled toprovide an oscillating pressure on, or flow of, the fluid to provide theoscillating flow within the channel.
 6. The system of claim 1, whereinthe fluid oscillator comprises a source of constant pressure or constantflow arranged and controlled to provide a constant pressure on, orconstant flow of, the fluid within the channel, and the fluid oscillatorfurther comprises two or more valves arranged along the channel andcontrolled to provide the oscillating flow within the channel betweenthe two or more valves by directing the constant pressure or flow fromthe source alternatingly at a first location along the channel and thenat a second location along the channel.
 7. The system of claim 6,wherein the fluid oscillator further comprises a signal generator and avalve driving circuit, and wherein the two or more valves comprisehigh-speed, three-way valves.
 8. The system of claim 1, wherein thechannel dimensions are configured and the flow rate of the fluid in thechannel is controlled such that a Reynolds number within the channel ineach direction of flow is from about 0.01 to
 2300. 9. (canceled)
 10. Thesystem of claim 1, wherein the frequency of oscillations is from about0.01 Hertz to about 100 Hertz.
 11. The system of claim 1, whereinparticles flowing within the fluid move a distance of 1.0 micron to 100cm in the first direction of flow, and then 1.0 micron to 100 cm in thesecond direction of flow. 12.-16. (canceled)
 17. The system of claim 2,wherein the hydraulic diameter (D_(h)) of the channel is selected toachieve a ratio of particle diameter a to D_(h) to be greater than 0.001and less than 1.0.
 18. The system of claim 2, wherein the channelcomprises a first section having a first hydraulic diameter, a secondsection in series with the first section and having a second hydraulicdiameter smaller than the first hydraulic diameter, and a third sectionin series with the second section and having a third hydraulic diameterlarger than the second hydraulic diameter.
 19. The system of claim 1,having at least one of the following parameters: a particle Reynoldsnumber (Re_(p)) greater than about 0.002; a channel Reynolds number (Re)less than about 2300; a channel hydraulic diameter (D_(h)) larger than aparticle diameter α; a ratio of particle diameter a to D_(h) less thanabout 1; and a Womersley number (Wo) less than about
 1. 20. A method forfocusing of particles in a fluid sample into one or more streamlineswithin a fluid flowing within a channel, the method comprisingintroducing into a channel a fluid comprising particles to be focused;and controlling a flow rate of the fluid in the channel to generate arepeating oscillating flow profile of the fluid in the channel, whereinthe flow profile includes at least one step in a first direction of flowand at least one step in a second direction of flow opposite to thefirst direction of flow, for a set period of time; thereby focusing theparticles into one or more streamlines within the fluid flowing withinthe channel.
 21. The method of claim 20, wherein the channel comprises amillimeter or micrometer channel.
 22. The method of claim 21, whereinthe dimensions of the channel and the flow rate are selected to provideinertial focusing.
 23. The method of claim 21, wherein the dimensions ofthe channel and the flow rate are selected to provide viscoelasticfocusing when a fluid in the channel is selected to have an appropriateviscoelasticity.
 24. The method of claim 20, wherein controlling a flowrate of the fluid comprises providing a source of pressure or flow andcontrolling the source of pressure or flow to provide the oscillatingflow within the channel.
 25. The method of claim 20, wherein controllingthe flow rate of the fluid comprises providing a source of constantpressure or constant flow controlled to provide a constant pressure on,or constant flow of, the fluid within the channel, controlling two ormore valves arranged along the channel, and providing an oscillatingflow within the channel between the two or more valves by directing theconstant pressure or flow from the source alternatingly at a firstlocation along the channel and then at a second location along thechannel.
 26. The method of claim 20, wherein the channel dimensions areselected, and the flow rate of the fluid in the channel is controlled,such that a Reynolds number within the channel in each direction of flowis from about 0.01 to
 2300. 27. (canceled)
 28. The method of claim 20,wherein the frequency of oscillations is from about 0.01 Hertz to about100 Hertz.
 29. The method of claim 20, wherein particles flowing withinthe fluid move a distance of 1.0 micron to 100 cm in the first directionof flow, and then 1.0 micron to 100 cm in the second direction of flow.30.-34. (canceled)
 35. The method of claim 20, wherein the hydraulicdiameter (D_(h)) of the channel is selected to achieve a ratio ofparticle diameter a to D_(h) to be greater than 0.001 and less than 1.0.36. The method of claim 20, wherein the flow rate is controlled toachieve at least one of the following parameters: a particle Reynoldsnumber (Re_(p)) greater than about 0.002; a channel Reynolds number (Re)less than about 2300; a channel hydraulic diameter (D_(h)) larger than aparticle diameter α; a ratio of particle diameter a to D_(h) less thanabout 1; and a Womersley number (Wo) less than about 1.